Research on single-pass forming width of JCOE longitudinal submerged arc welded pipe

Abstract

JCOE longitudinal submerged arc welded pipes are widely used in oil and gas transportation, but their JCO forming process suffers from low efficiency due to the lack of precise guidance on single-pass forming width. This study focuses on optimizing this key parameter through theoretical analysis, numerical simulation, and experimental validation. Based on medium plate bending mechanics and considering springback, a theoretical model is established. Under fixed force and lower die opening, analytical expressions for single-pass forming central angle and width are derived. Using ABAQUS, the cold bending process is simulated, and experiments are conducted on a 3600T bending unit. Results show consistent trends between theoretical, simulation, and experimental data, with a maximum error of 11.4% between theory and experiments. Corrected theoretical expressions can guide the determination of process parameters like step length and forming passes in practical production. It provides a theoretical basis and technical support for improving weld pipe quality, enhancing production efficiency, and reducing costs.

Introduction

The JCO forming process is a widely used manufacturing technique for large-diameter longitudinal submerged arc welded pipes in oil and gas transportation. Its forming characteristics include progressive multi-step die pressing, offering advantages such as relatively low investment, high reliability, and flexible production organization, However, its production efficiency is relatively low¹. Therefore, starting from basic theories, a research is conducted on the single-pass forming width that affects the forming efficiency.

Numerous scholars have conducted extensive researches on the JCO forming process, focusing on forming force, springback angle, and die curvature. These studies have achieved significant results and provided guidance for die curvature design and optimization. For instance, studies^2,3 addressed the issue of significant roundness errors in pipes caused by reliance on empirical methods during JCO forming. By applying bending theory and adopting a bilinear hardening material model, they established analytical formulas for single-bending process parameters in JCO forming and validated the theoretical bending model through experimental methods. Study⁴ developed a mathematical model under the assumptions that cross-sections remain planar and the neutral layer remains unchanged before and after forming. It concluded that, for materials of the same type, the springback angle decreases with increasing wall thickness. Research by Zhao Jun’s team at Yanshan University^5–9, along with studies^10,11, utilized the finite element method to simulate the JCO bending process for large-diameter longitudinal submerged arc welded pipes. These works analyzed stress-strain field distributions under different upper die curvature radii, derived force-displacement curves, and established relationships between forming force and target bending angles for varying punch radii. Additionally, they optimized process parameters using a feed forward neural network model for intelligent control of wide-plate free bending and developed a computer-aided process planning system for JCO forming of large longitudinal welded pipe blanks.

While existing studies aim to improve forming precision and enable computer-aided calculation of process parameters, their studies are all based on the traditional bending method, without considering the relationship between width deformation and forming force in the JCO forming process, nor involving the most critical effective width of single forming in the forming process. Therefore, this paper will focus on discussing the single forming width that affects forming force, forming accuracy and forming efficiency.

Theoretical analysis of JCO Single-Pass forming width

As a typical application of the free bending plastic forming process, JCO forming introduces the following assumptions for the convenience of theoretical analysis: Before and after bending, the cross-section of the medium plate in the deformation zone (the plane perpendicular to the fiber direction) remains a plane; The thickness and width of the medium plate remain unchanged before and after bending, and the position of the stress neutral layer is still in the middle of the medium plate; It is assumed that there is no extrusion between the longitudinal fibers of the medium plate during the bending process, there is no transverse stress between the fibers, and each fiber in the medium plate is in a state of unidirectional tension or unidirectional compression stress; The tangential stress and tangential strain of the inner and outer layers are completely consistent with the stress-strain relationship in the unidirectional tension state; The true stress-strain curve of the material obeys the linear elastic-plastic strengthening law.

The diagram of the medium plate bending is shown in Fig. 1. In the figure, the thickness of the medium plate part is t, the distance between the lower dies is L. Under the action of the bending force P, the plate is bent into an arc with a curvature of R, and its central angle is ɑ. A is the horizontal projection of the deformation zone after bending and forming.

Fig. 1.

Diagram of medium plate Bending.

Calculation of the curvature of the upper die

This is a free bending forming method with a bottomless lower die. There are many factors that affect the final bending shape of the plate, and these factors are interrelated and influence each other, including: the curvature of the die, process parameters, the actual performance and geometric dimensions of the material, etc. Among them, the first thing to determine is the die curvature R. Currently, there is no method that can accurately express it. Therefore, a commonly used expression¹² is adopted for calculation of the upper die radius:

1

In the formula: R_m — Radius of curvature of the upper die; R — Radius after springback; t — Wall thickness of the pipe; D — Plastic hardening modulus of the material; E — Elastic modulus of the material; σ_s — Yield limit of the material; µ— Poisson’s ratio.

Analysis of the single deformation width

During the bending process of the medium plate, the material in the deformation zone is in a state of high - level plastic deformation and bends around the center line by an angle. On the outer surface of the bending zone, in some cases, tiny cracks may also appear. Except for the area near the center layer on the cross - section of the deformation zone, the stress is close to the tensile strength of the material. The upper part of the neutral layer is under compression, and the lower part is under tension. The bending moment¹² on the cross - section of the deformation zone is:

2

The bending moment generated by the bending force in the deformation zone is:

3

From , the forming force is:

4

5

In the formula: P —— Forming force; l —— Length of the medium plate; V —— Width of the opening of the lower die;

A —— Width of the horizontal projection of the bending deformation zone,; R —— Inner radius when the medium plate is bent; ɑ —— Forming central angle;σ_b —— Tensile strength.

From the above formula, the relationship between the forming force and the forming central angle is obtained. The larger the central angle is, the larger the width of a single deformation will be. In order to improve the production efficiency, the forming central angle must be increased. When the forming force and the width of the lower die are fixed, the forming central angle can be accurately obtained through the above formula. Then, the width of a single deformation can be further calculated as:

6

S—— The Single Deformation Width.

Thus, a theoretical expression for the JCO single-pass forming width is established, which established a relationship between the forming force P and the single-pass forming width. By substituting specific values into the above expression, the single-pass forming width can be obtained.

Numerical simulation of the forming process

To verify the theoretical expression for the JCO single-pass forming width, Analyze the forming process of the steel pipe by using ABAQUS 6.14 software (https://www.3ds.com/products-services/simulia/products/abaqus). The simulation model is shown in Fig. 2. The hardness and deformation of the upper die and lower die are significantly greater than those of the forming material.Therefore, they are set as rigid bodies. The radius of curvature of the upper die is derived from Eq. (1), and its value varies when producing pipes of different specifications, and the dimension of the radius of lower die is 100 mm. Table 1 shows the basic parameters of the equipment, and Table 2 shows the material properties and geometric parameters of the forming material. The radius of the upper die is a value calculated according to Eq. (1) and then rounded.

Fig. 2.

Finite Element Model of the Cold Bending Forming Process. The 3D image in Fig. 2 was generated in simulation software (ABAQUS). ABAQUS version number is 6.14 and URL link is https://www.3ds.com/products-services/simulia/products/abaqus.

Table 1.

The basic parameters of equipment.

Parameter	Value
Total equipment pressure / T	3600
Length of upper and lower dies / mm	12,500
Width of upper die / mm	240
Radius of lower die / mm	100
Opening of lower die / mm	220
Static friction coefficient	0.35
Dynamic friction coefficient	0.25

Table 2.

Material properties and geometric parameters of the forming Material.

No.	Diameter X Thickness /mm	Material	Plate Width /mm	Yield Strength༏MPa	Tensile Strength༏MPa
1	Φ610 × 7.95	S355J0H	1890	355	470
2	Φ711 × 10	L245	2112	245	415
3	Φ813 × 12.75	L290	2593	290	430
4	Φ914 × 12.75	X42	2828	289	414
5	Φ1016 × 13.9	X42	3146	289	414
6	Φ1219 × 15.8	X52	3778	358	448
7	Φ1422 × 13.9	X52	4420	358	448

Seven specifications that can be verified by experiments are selected for simulation. The steel pipe specifications (diameter × wall thickness) are as follows: Φ610 × 7.95 mm, Φ711 × 10 mm, Φ813 × 12.75 mm, Φ914 × 12.75 mm, Φ1016 × 13.9 mm, Φ1219 × 15.8 mm, Φ1422 × 13.9 mm.

During the simulation process, the upper die is applied a certain displacement to press some areas of the plate into a specific curvature, and the reaction force exerted on the upper die by the deformation of the plate is close to 3600T. Then, the curvature value and the width of the deformation zone are measured, so that the single forming width can be determined. To verify whether this result can be applied to actual production, it is also necessary to conduct an overall planning of process parameters such as step length and number of forming steps according to the finished product specifications and the rule that the number of pressing operations in JCO forming can only be an odd number. After that, the full-process simulation of pipe forming is carried out, as shown in Fig. 3.

Fig. 3.

Simulation of the JCO Forming Process. The 3D image in Fig. 3 was generated in simulation software (ABAQUS). ABAQUS version number is 6.14 and URL link is https://www.3ds.com/products-services/simulia/products/abaqus.

It can be seen from Fig. 3 that when loading, the medium plate between the two lower dies and the upper die undergoes deformation, which consists of two parts: plastic deformation and elastic deformation. The part that reaches the yield limit of the corresponding material undergoes plastic deformation, and the material in the transition zone remains in elastic deformation. After unloading, due to the stress balance inside the material, residual deformation occurs, and the curvature after deformation is the target curvature. The deformation that remains in the end is the object of key concern. The first diagram in the figure shows the “J” forming process, the second diagram shows the “C” forming process, and the third diagram shows the “O” forming process.

Experiment on the forming process

The experiment was carried out on the 3600T bending unit of Haiqianwei Company, as shown in Fig. 4. The experimental research was carried out during the trial production stage according to the company’s orders. To ensure the reliability of the production process, 3 tests are conducted for each specification during the trial production, and the test result is the average value of the 3 tests.The forming force during the forming process was collected by the hydraulic pressure sensor installed on the equipment hydraulic system. The curvature during the forming process was detected by a standard profile gauge and rechecked by the three-point method. A ruler was used to measure the forming width.

Fig. 4.

Experimental Site of Φ711 × 10.

According to the forming results of theoretical analysis and simulation, the process of the experiment is planned, including the curvature of the upper die, the number of forming steps, the step size, and the amount of press-down. These data are applied in the experiment. On the premise that the roundness after forming meets the production process control standard, the relevant data are measured on-site.

In order to reduce the impact of repeated pressing on the material, the every two deformation zones are preferably tangent or alternate. Considering the feasibility of the actual production process planning, the forming step size in the experiment is larger than the forming width calculated by theory and simulation, so that the two bending formations are separated by 0 to 15 mm. The straight part that has not been deformed will be processed in the subsequent expanding process.

Results and discussion

When the external conditions such as forming force and lower die opening width are fixed, the central angles and forming widths corresponding to the single-pass forming of the above seven specifications are obtained by applying expressions (5) and (6) from the theoretical analysis, and the results are shown in Table 3.

Table 3.

Deformation curvature and width of the medium Plate.

No.	Diameter X Thickness /mm	Material	Forming Width /mm	Central Angle/o
1	Φ610 × 7.95	S355JOH	216.98	52
2	Φ711 × 10	L245	217.02	43.05
3	Φ813 × 12.75	L290	198.9	30.528
4	Φ914 × 12.75	X42	199.12	26.265
5	Φ1016 × 13.9	X42	192.9	23.4
6	Φ1219 × 15.8	X52	175.12	18.9
7	Φ1422 × 13.9	X52	185.43	17.808

It is found that the pipe diameter, wall thickness and material all affect the forming width. For the same pipe diameter and material, the larger the wall thickness, the smaller the forming width. For materials of the same specification, the higher the yield strength, the smaller the forming width. For the same material and wall thickness, the pipe diameter has little influence on the forming width. Among them, the wall thickness has the greatest influence on the forming width.

Based on the theoretical results and the long-term application experience of the project team, the actual forming process parameters for the above seven specifications were planned (see Table 4), followed by numerical simulations and on-site experiments. Both successfully achieved JCO forming, with their roundness and opening degree meeting the on-site production requirements. The difference lies in the transition part between two consecutive forming operations, where the on-site experimental results are significantly smaller than those of the numerical simulations.

Table 4.

Actual forming main process Parameters.

No.	Diameter X Thickness /mm	Material	Upper Die Radius /mm	Step	Step Length /mm
1	Φ610 × 7.95	S355JOH	245	7	200
2	Φ711 × 10	L245	310	9	210
3	Φ813 × 12.75	L290	375	11	190
4	Φ914 × 12.75	X42	420	13	190
5	Φ1016 × 13.9	X42	485	15	180
6	Φ1219 × 15.8	X52	560	21	165
7	Φ1422 × 13.9	X52	635	23	175

The data of forming widths obtained from theoretical analysis, simulation, and experimental results are compiled in Table 5. It can be seen from the table that, under the condition of a fixed lower die opening, when the equipment capacity is fully utilized, the forming width reaches 165–210 mm. In contrast, the forming width planed by the traditional empirical method is generally 50–120 mm. Through process optimization, the number of forming steps can be reduced by 32%-53%, which not only effectively improves production efficiency but also reduces energy consumption.

Table 5.

Statistics of the forming Width.

No.	Diameter X Thickness /mm	Material	Plate Width /mm	Forming Width /mm
				Theoretical	Simulation	Experiment
1	Φ610 × 7.95	S355JOH	1890	216.98	198.6	193.4
2	Φ711 × 10	L245	2112	217.02	211.4	202.8
3	Φ813 × 12.75	L290	2593	198.9	191	179.2
4	Φ914 × 12.75	X42	2828	199.12	193.3	178.5
5	Φ1016 × 13.9	X42	3146	192.9	182.8	171.3
6	Φ1219 × 15.8	X52	3778	175.12	168.6	160.4
7	Φ1422 × 13.9	X52	4420	185.43	179.2	168.8

It can also be found that the theoretical value is larger than the simulation value, with a maximum error of 8.5%. This may be due to the assumption and simplification of the model during theoretical analysis. The theoretical value is also larger than the experimental result, with a maximum error of 11.4%. This is caused by factors such as uneven thickness of the plate, differences in the strength of the same plate, and equipment issues during the actual production process.

According to the theoretical analysis, simulation, and experimental measurement of the forming width, curves under appropriate process conditions for corresponding specifications and materials are plotted, as shown in Fig. 5. In the figure, the abscissa values are 1, 2, 3, 4, 5, 6, 7, corresponding to the specifications of Φ610 × 7.95 mm, Φ711 × 10 mm, Φ813 × 12.75 mm, Φ914 × 12.75 mm, Φ1016 × 13.9 mm, Φ1219 × 15.8 mm, and Φ1422 × 13.9 mm respectively; the ordinate represents the forming width values obtained from theoretical analysis, simulation, and experimental measurement. Series 1 represents the forming width values from theoretical analysis, Series 2 represents the forming width values from simulation, and Series 3 represents the forming width values from experimental measurement.

Fig. 5.

Forming width curve.

It can be seen from the figure that the theoretical analysis values for various specifications are greater than the simulation values, and the simulation values are greater than the experimental measurement values. Their changing trends are consistent, with a maximum error of 11.4%. In this way, the theoretical calculation can relatively accurately reflect the actual deformation. This calculation method can guide actual production, determine the forming step size and the number of forming times, make full use of the performance of the equipment, and accurately estimate the annual output of the equipment.

Conclusion

A simplified analytical method was adopted, taking into account factors such as springback of the material after bending, and combined with the calculation formula of the free cold bending forming die, a mechanical analysis of the steel pipe forming process was carried out. Through the analysis, the expressions for the single-pass forming central angle and forming width under the conditions of fixed force and fixed opening of the lower die were obtained. This relationship, rarely reported in previous qualitative studies, provides a precise basis for process parameter optimization.

The finite element simulations (ABAQUS) and experiments were carried out. Experimental verification on a 3600T bending unit. The results showed the experimental results are the smallest, while the theoretical analysis results are the largest, with a maximum error of 11.4%. The theoretical expressions can be used to guide practical production after being appropriately revised. Than the number of forming steps for production can be optimized and reduced by 32%-53%. This directly enhances production efficiency, demonstrating the research’s practical significance for cost-control and quality improvement.

This study primarily focuses on carbon steel and low-alloy steel pipes under room-temperature conditions, without considering the effects of extreme temperatures or material fatigue on forming width. Future research will extend to multi-material composite pipes forming and explore intelligent parameter prediction models by integrating machine learning, aiming to further improve the adaptability of the theoretical framework.

Author contributions

Mingjun Wen analyzed the forming principles, established the theoretical model, and derived the expressions for the single - pass forming central angle and width. Xin Zhang conducted the numerical simulation of the forming process and analyzed the errors between theoretical analysis and experimental results. Caizhong Shang carried out the experimental research on existing equipment. Mingjun Wen and Xin Zhang wrote the main manuscript text. Caizhong Shang prepared the relevant figures. All authors reviewed the manuscript.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.